CN105809249A - Double neural network-based PM2.5 concentration detection and prediction system and method - Google Patents

Abstract

The invention relates to a double neural network-based PM2.5 concentration detection and prediction system. The double neural network-based PM2.5 concentration detection and prediction system includes a data acquisition and storage unit, a first neural network unit and a second neural network unit; the data acquisition and storage unit includes a light scattering principle-based PM2.5 sensor; the first neural network unit includes a BP neural network; the second neural network unit mainly comprises a data preprocessing unit and a radial basis function neural network; and in the data acquisition and storage unit, the PM2.5 sensor is set to measure PM2.5 concentration values with a set time interval and upload the PM2.5 concentration values to a computer as measurement data, so that the PM2.5 concentration values can be stored, and the PM2.5 sensor is also set to acquire PM2.5 concentration values which are officially updated at the same time point and store the PM2.5 concentration values as standard data. The double neural network-based PM2.5 concentration detection and prediction system and method provided by the invention can realize accurate localization measurement and effective prediction.

Description

A kind of PM2.5 Concentration Testing based on amphineura network and prognoses system and method

Technical field

The invention belongs to Detection of Air Quality field, particularly relate to a kind of PM2.5 concentration detection system and Forecasting Methodology.

Background technology

PM is the abbreviated form of English ParticulateMatter (particulate matter).PM2.5 is the diameter particulate matter less than or equal to 2.5 microns, maybe can enter lung particulate matter also referred to as fine particle.Due to PM2.5 can the long period suspension in atmosphere, the remote scope of propagation distance greatly and easily attach poisonous and harmful substances, so human health and air quality are had significant impact by it.

The method measuring PM2.5 is broadly divided into 3 kinds: gravimetric method, β attenuation sensors and trace oscillating balance method.It is big that these three measuring method measures difficulty, and cost is high, is difficult to large-scale promotion and uses.It is more the PM2.5 detector of the principle utilizing light scattering on the market, because its cost is low, measures simple.But utilizing light scattering apparatus to measure PM2.5 concentration value, its degree of accuracy is relatively low.Because the relation between scattering of light and particle concentration is very uncertain, it is subject to the impact of factors, for instance the chemical composition of particulate matter, shape, proportion, particle size distribution, and these both depend on the composition of polluter.This means that the reduction formula between light scattering and particle concentration is all likely to becoming whenever and wherever possible.Accordingly, it would be desirable to instrument user is constantly corrected with standard method.

For solving the problems referred to above, equality people is kept in patent " the PM2.5 concentration detection method based on interval radial basis function neural network " in pass, the shortcoming that solution matrix equation algorithm computing is difficult, precision is relatively low is overcome by setting up radial basis function neural network, it is possible not only to detection PM2.5 concentration effectively, it is also possible to detect which scope is the PM2.5 concentration of detection float within probabilistic condition；Xu Lin et al. is in patent " PM2.5 concentration detection method and device based on neutral net ", by setting up regularization neural network model, exports PM2.5 concentration value.The method overcoming the shortcoming that in prior art, PM2.5 concentration detection method automaticity is low, and be capable of duplicate detection, accuracy of detection is high；Zhu Hong et al. is in paper " polluting signal analysis detection based on the PM2.5 improving neural network algorithm ", the training invited by introducing fault-tolerance theory well to prevent network to enter plateau in the training process in BP neutral net stops, it is thus possible to training network smoothly, PM2.5 concentration value can be detected preferably；PM2.5 concentration value all can be detected by above detection system preferably, but the source of sample data is required higher and is not previously predicted function.

PM2.5 concentration value, in paper " the fuzzy neural network PM2.5 concentration prediction based on modified model PSO ", is had good predictive ability by the fuzzy neural network of modified model PSO by Ma Tiancheng et al.；PM2.5 concentration value, in paper " the PM2.5 forecast model based on neutral net ", has been carried out good prediction by setting up BP neural network model by Zhang Yiwen et al.；Yang Qikai et al. is in paper " evolutionary model occurs the PM2.5 based on genetic algorithm with BP neutral net ", by using the neutral net of genetic algorithm that PM2.5 concentration value is also had good prediction.Above prognoses system all has good predictive ability, but the sample data kind that they require is many, and accuracy is high, and the requirement of sample data is very harsh, is difficult to meet popular routine use demand.

Summary of the invention

In order to overcome the deficiency that cannot realize accurately localizing measurement and prediction of existing existing PM2.5 concentration value metering system, the present invention provides a kind of and realizes accurate localization measurement and the PM2.5 Concentration Testing based on amphineura network effectively predicted and prognoses system and method.

The technical solution adopted for the present invention to solve the technical problems is:

A kind of PM2.5 Concentration Testing based on amphineura network and prognoses system, described system includes data acquisition memory element, first nerves NE and nervus opticus NE, described data acquisition memory element includes the PM2.5 sensor based on light scattering principle, described first nerves network includes BP neutral net, and described nervus opticus network mainly includes data pre-processing unit and radial base neural net；

In described data acquisition memory element, setting PM2.5 sensor and upload to computer as measurement data to set time interval measurement PM2.5 concentration value and store, the PM2.5 concentration value simultaneously gathering the renewal of synchronization official as normal data and stores；

In described first nerves NE, the measurement data recorded by described PM2.5 sensor inputs data as sample and is input to the first nerves network trained, by the measurement data that the output obtained after the first nerves network that trains is exactly localization, the measurement data of output localization, is stored to array simultaneously；

In described nervus opticus NE, after the number of elements in the array of the measurement data of described storage localization reaches N, this array element starts to be delivered to scroll mechanism；

Described scroll mechanism is as follows: after the number of elements in the array of the measurement data of described storage localization reaches N, scroll mechanism starts to read N number of data up-to-date in array, namely, when there being new element to be stored in, scroll mechanism can re-read up-to-date N number of data automatically；

Described up-to-date N number of data being normalized by normalization, it is interval that the data after normalization are distributed in [0.1,0.9]；

According to gray model, the data after described normalization are passed through the Accumulating generation new data sample data as radial base neural net；

It is input to, as sample input data, the nervus opticus network trained by the new data after gray model Accumulating generation using described, matching through nervus opticus network obtains fitting data, this fitting data is carried out renormalization process and final prediction data can be obtained, this prediction data is stored and exports.

A kind of PM2.5 Concentration Testing based on amphineura network and Forecasting Methodology, described method comprises the steps:

1) data acquisition and storage

Setting PM2.5 sensor upload to computer as measurement data to set time interval measurement PM2.5 concentration value and store, the PM2.5 concentration value simultaneously gathering the renewal of synchronization official as normal data and stores；

2) first nerves network processes

The measurement data recorded by described PM2.5 sensor inputs data as sample and is input to the first nerves network trained, by the measurement data that the output obtained after the first nerves network that trains is exactly localization, the measurement data of output localization, is stored to array simultaneously；3) nervus opticus network processes

After number of elements in the array of the measurement data of described storage localization reaches N, this array element starts to be delivered to scroll mechanism；

Described scroll mechanism is as follows:

After number of elements in the array of the measurement data of described storage localization reaches N, scroll mechanism starts to read N number of data up-to-date in array, and namely when there being new element to be stored in, scroll mechanism can re-read up-to-date N number of data automatically；

Described up-to-date N number of data being normalized by normalization, it is interval that the data after normalization are distributed in [0.1,0.9]；

According to gray model, the data after described normalization are passed through the Accumulating generation new data sample data as radial base neural net；

It is input to, as sample input data, the nervus opticus network trained by the new data after gray model Accumulating generation using described, matching through nervus opticus network obtains fitting data, this fitting data is carried out renormalization process and final prediction data can be obtained, this prediction data is stored and exports.

Further, described step 2) in, the training step of described first nerves network includes:

Step 2.1, the data collection interval setting PM2.5 sensor and times of collection, data collection interval and times of collection collection according to setting organize measurement data more, gather the official standard data that many groups synchronize, using training data as BP neutral net of described measurement data and normal data simultaneously；

Step 2.2, set BP neutral net as three layers: input layer, hidden layer and output layer, set the node number of input layer and hidden layer, and it is identical with input layer to set output layer node number.

Step 2.3, setting the transmission function of hidden layer as Log-Sigmiod function, the transmission function of output layer is linear function, and wherein Log-Sigmiod function computing formula is as follows:

$\log sig\left(n\right)=\frac{1}{1+e^{-n}}$

Step 2.4, with little random number, weights and biasing are initialized, to ensure that Network Dept. is saturated by big weights input, concurrently set the anticipation error minima of network, maximum iteration time and learning rate；

The normal data of described official, as input, is input to BP neutral net as target by step 2.5, the measurement data recorded by described PM2.5 sensor, calculates error, according to error transfer factor weights；

Step 2.6, judge whether convergence, when error is less than anticipation error minima, algorithmic statement；Or terminate algorithm when reaching maximum iteration time；

Step 2.7, input training data carry out simulating, verifying, it is determined that network training completes.

Further, described step 3) in, the training step of described nervus opticus network includes:

Step 3.1, by being obtained the measurement data of corresponding localization by the BP neutral net that trains by the measurement data of PM2.5 sensor acquisition, the normal data of the measurement data of localization and collection is all normalized and obtains measurement data and normal data after normalization.Normalization formula is as follows:

$y=0.1+\frac{0.8(x-x_{\min })}{(x_{max}-x)}$

In formula: x is the measurement data of described localization, x_minAnd x_maxRespectively often organizing the minima in data and maximum, y is the measurement data after normalization, is distributed in [0.1,0.9] interval；

Step 3.2, according to gray model, by the measurement data after described normalization by one group of new data of Accumulating generation, Accumulating generation formula is as follows:

Measurement data after note normalization is:

X⁽⁰⁾={ x⁽⁰⁾(1),x⁽⁰⁾(2),...x⁽⁰⁾(n)}

New data after note Accumulating generation is:

X⁽¹⁾={ x⁽¹⁾(1),x⁽¹⁾(2),...x⁽¹⁾(n)}

Wherein

$X^{\left(1\right)}\left(k\right)=\underset{i=1}{\overset{k}{\Σ}}{x}^{\left(0\right)}\left(i\right),k=1,2,\mathrm{...}n.$

Using this new data training data as radial base neural net；

Step 3.3, set radial base neural net as three layers: input layer, hidden layer and output layer, set the node number of input layer and hidden layer, and set output layer as a node.

Step 3.4, setting the excitation function of hidden layer as Gaussian function, set the transmission function of output layer as linear function, wherein Gaussian function formula is as follows:

$\mathrm{\φ}\left(\right||X_k-X_i|\left|\right)=\exp (-\frac{n}{{d_{\max }}^2}||X_k-X_i|{|}^2),i=1,2,\mathrm{...},n$

In formula: X_kFor training sample, X_iFor individual cluster centre, d_maxFor the ultimate range between selected center, n is the node number of hidden layer；

Output result is as follows:

$y=\underset{i=1}{\overset{N}{\Σ}}{\mathrm{\ω}}_i\mathrm{\φ}(X_k,X_i)-x^{\left(1\right)}\left(n\right)$

Step 3.5, being inputted as the sample of radial base neural net by the described new data by obtaining after gray model Accumulating generation, normalization normal data exports as target, and radial base neural net is trained；

Step 3.6, choose cluster centre by K-means clustering algorithm.Several different samples are randomly choosed as initial cluster centre inputting from described sample, one sample of stochastic inputs, calculates this input sample nearest apart from which cluster centre, just it is classified as the same class of this cluster centre, repetitive operation, updates cluster centre；

Whether step 3.7, evaluation algorithm restrain, when cluster centre no longer changes or the threshold value less less than, and algorithmic statement.If it is determined that not convergence, otherwise forward step 5 to and continue iteration, the cluster centre finally determined during end；

Step 3.8, determine cluster centre after, with the new data obtained by gray model as input, normalized normal data as output training network, study obtain standard deviation and weights, wherein standard deviation formula is as follows:

$\mathrm{\σ}=\frac{d_{max}}{\sqrt{2n}}$

Step 3.9, input training data carry out simulating, verifying, it is determined that network training completes.

Beneficial effects of the present invention is mainly manifested in: overcomes PM2.5 sensor and cannot adapt in the problem how measured, make it can obtain measurement result comparatively accurately under different geographical environment, realize localization to measure, it is simultaneously achieved the prediction to following short time interval PM2.5 concentration value, is conducive to the timely expansion of prevention work.

Accompanying drawing explanation

Fig. 1 is based on the PM2.5 Concentration Testing of amphineura network and the schematic diagram of prognoses system.

Fig. 2 is based on the PM2.5 Concentration Testing of amphineura network and the schematic diagram of Forecasting Methodology.

Fig. 3 is the training flow chart of BP neutral net.

Fig. 4 is the training flow chart of RBF neural.

Detailed description of the invention

Below in conjunction with accompanying drawing, the invention will be further described.

With reference to Fig. 1～Fig. 4, a kind of PM2.5 concentration detection system based on amphineura network and prognoses system, including: data acquisition memory element, first nerves NE and nervus opticus NE, the described main sampler of data acquisition memory element is the PM2.5 sensor of the principle utilizing light scattering.Described first nerves network mainly includes the neutral net that have employed error backpropagation algorithm (ErrorBackPropagation, BP), is called for short BP neutral net.Described nervus opticus network mainly includes data pre-processing unit and radial base neural net.

With reference to Fig. 2, include based on the PM2.5 concentration detection system of amphineura network and the idiographic flow of Forecasting Methodology:

Setting PM2.5 sensor uploaded to computer using one hour for time interval measurement PM2.5 concentration value as measurement data and store, the PM2.5 concentration value simultaneously gathering the renewal of synchronization official as normal data and stores；

In the embodiment of the present invention, the measurement data of collection and normal data such as table 1:

Table 1

The measurement data recorded by described PM2.5 sensor inputs data as sample and is input to the first nerves network trained, by the measurement data that the output obtained after the first nerves network that trains is exactly localization, the measurement data of output localization, is stored to array simultaneously；

With reference to Fig. 3, described in the training step of first nerves network that trains include:

Step 2.1, set the data collection interval of PM2.5 sensor as 1 hour and times of collection as 24 times, data collection interval and times of collection according to setting gather 24 groups of measurement data, gather 24 groups of official standard data synchronized, using training data as BP neutral net of described measurement data and normal data simultaneously；

Step 2.2, setting BP neutral net as three layers: input layer, hidden layer and output layer, set the node number of input layer and output layer as 1, the node number of hidden layer is 5.

Step 2.3, setting the transmission function of hidden layer as Log-Sigmiod function, the transmission function of output layer is linear function, and wherein Log-Sigmiod function computing formula is as follows:

$\log sig\left(n\right)=\frac{1}{1+e^{-n}}$

Step 2.4, with little random number, weights and biasing being initialized, to ensure that Network Dept. is saturated by big weights input, the anticipation error minima concurrently setting network is 0.1, maximum iteration time be 5000 and learning rate be 0.1；

The normal data of described official, as input, is input to BP neutral net as target by step 2.5, the measurement data recorded by described PM2.5 sensor, calculates error, according to error transfer factor weights；

Step 2.6, judge whether convergence, when error is less than anticipation error minima, algorithmic statement；Or terminate algorithm when reaching maximum iteration time；

Step 2.7, input training data carry out simulating, verifying, it is determined that network training completes；

After number of elements in the array of the measurement data of described storage localization reaches 10, this array element starts to be delivered to scroll mechanism；

Described scroll mechanism function is as follows:

After number of elements in the array of the measurement data of described storage localization reaches 10, scroll mechanism starts to read 10 data up-to-date in array, and namely when there being new element to be stored in, scroll mechanism can re-read up-to-date 10 data automatically；

Described 10 up-to-date data being normalized by normalization, it is interval that the data after normalization are distributed in [0.1,0.9]；

According to gray model, the data after described normalization are passed through the Accumulating generation new data sample data as radial base neural net；

It is input to, as sample input data, the nervus opticus network trained by the new data after gray model Accumulating generation using described, matching through nervus opticus network obtains fitting data, this fitting data is carried out renormalization process and final prediction data can be obtained, this prediction data is stored and exports；

With reference to Fig. 4, described in the training step of nervus opticus network that trains include:

Step 3.1, by being obtained the measurement data of corresponding localization by the BP neutral net that trains by the measurement data of PM2.5 sensor acquisition, the normal data of the measurement data of localization and collection is all normalized and obtains measurement data and normal data after normalization.Normalization formula is as follows:

$y=0.1+\frac{0.8(x-x_{\min })}{(x_{max}-x)}$

In formula: x is the measurement data of described localization, x_minAnd x_maxRespectively often organizing the minima in data and maximum, y is the measurement data after normalization, is distributed in [0.1,0.9] interval；

Step 3.2, according to gray model, by the measurement data after described normalization by one group of new data of Accumulating generation, Accumulating generation formula is as follows:

Measurement data after note normalization is:

X⁽⁰⁾={ x⁽⁰⁾(1),x⁽⁰⁾(2),...x⁽⁰⁾(n)}

New data after note Accumulating generation is:

X⁽¹⁾={ x⁽¹⁾(1),x⁽¹⁾(2),...x⁽¹⁾(n)}

Wherein

$X^{\left(1\right)}\left(k\right)=\underset{i=1}{\overset{k}{\Σ}}{x}^{\left(0\right)}\left(i\right),k=1,2,\mathrm{...}n.$

Using this new data training data as radial base neural net；

Step 3.3, set radial base neural net as three layers: input layer, hidden layer and output layer, set the node number of input layer as 9 and the node number of hidden layer as 15, and set output layer as 1 node.

Step 3.4, setting the excitation function of hidden layer as Gaussian function, set the transmission function of output layer as linear function, wherein Gaussian function formula is as follows:

$\mathrm{\φ}\left(\right||X_k-X_i|\left|\right)=\exp (-\frac{n}{{d_{\max }}^2}||X_k-X_i|{|}^2),i=1,2,\mathrm{...},n$

In formula: X_kFor training sample, X_iFor individual cluster centre, d_maxFor the ultimate range between selected center, n is the node number of hidden layer；

Output result is as follows:

$y=\underset{i=1}{\overset{N}{\Σ}}{\mathrm{\ω}}_i\mathrm{\φ}(X_k,X_i)-x^{\left(1\right)}\left(n\right)$

Step 3.5, being inputted as the sample of radial base neural net by the described new data by obtaining after gray model Accumulating generation, normalization normal data exports as target, and radial base neural net is trained.

Step 3.6, choose cluster centre by K-means clustering algorithm.Several different samples are randomly choosed as initial cluster centre inputting from described sample, one sample of stochastic inputs, calculates this input sample nearest apart from which cluster centre, just it is classified as the same class of this cluster centre, repetitive operation, updates cluster centre；

Whether step 3.7, evaluation algorithm restrain, when cluster centre no longer changes or the threshold value less less than, and algorithmic statement.If it is determined that not convergence, otherwise forward step 5 to and continue iteration, the cluster centre finally determined during end；

Step 3.8, determine cluster centre after, with the new data obtained by gray model as input, normalized normal data as output training network, study obtain standard deviation and weights, wherein standard deviation formula is as follows:

$\mathrm{\σ}=\frac{d_{max}}{\sqrt{2n}}$

Step 3.9, input training data carry out simulating, verifying, it is determined that network training completes；

Localization measurement data and prediction data such as table 2, table 3 is obtained according to above operation:

Table 2

Table 3.

Claims (4)

1. the PM2.5 Concentration Testing based on amphineura network and prognoses system, it is characterized in that: described system includes data acquisition memory element, first nerves NE and nervus opticus NE, described data acquisition memory element includes the PM2.5 sensor based on light scattering principle, described first nerves network includes BP neutral net, and described nervus opticus network mainly includes data pre-processing unit and radial base neural net；

In described data acquisition memory element, setting PM2.5 sensor and upload to computer as measurement data to set time interval measurement PM2.5 concentration value and store, the PM2.5 concentration value simultaneously gathering the renewal of synchronization official as normal data and stores；

In described first nerves NE, the measurement data recorded by described PM2.5 sensor inputs data as sample and is input to the first nerves network trained, by the measurement data that the output obtained after the first nerves network that trains is exactly localization, the measurement data of output localization, is stored to array simultaneously；

In described nervus opticus NE, after the number of elements in the array of the measurement data of described storage localization reaches N, this array element starts to be delivered to scroll mechanism；

Described scroll mechanism is as follows: after the number of elements in the array of the measurement data of described storage localization reaches N, scroll mechanism starts to read N number of data up-to-date in array, namely, when there being new element to be stored in, scroll mechanism can re-read up-to-date N number of data automatically；

Described up-to-date N number of data being normalized by normalization, it is interval that the data after normalization are distributed in [0.1,0.9]；

According to gray model, the data after described normalization are passed through the Accumulating generation new data sample data as radial base neural net；

It is input to, as sample input data, the nervus opticus network trained by the new data after gray model Accumulating generation using described, matching through nervus opticus network obtains fitting data, this fitting data is carried out renormalization process and final prediction data can be obtained, this prediction data is stored and exports.

2. the PM2.5 Concentration Testing based on amphineura network and Forecasting Methodology, it is characterised in that:

Described method comprises the steps:

1) data acquisition and storage

Setting PM2.5 sensor upload to computer as measurement data to set time interval measurement PM2.5 concentration value and store, the PM2.5 concentration value simultaneously gathering the renewal of synchronization official as normal data and stores；

2) first nerves network processes

The measurement data recorded by described PM2.5 sensor inputs data as sample and is input to the first nerves network trained, by the measurement data that the output obtained after the first nerves network that trains is exactly localization, the measurement data of output localization, is stored to array simultaneously；3) nervus opticus network processes

After number of elements in the array of the measurement data of described storage localization reaches N, this array element starts to be delivered to scroll mechanism；

Described scroll mechanism is as follows:

After number of elements in the array of the measurement data of described storage localization reaches N, scroll mechanism starts to read N number of data up-to-date in array, and namely when there being new element to be stored in, scroll mechanism can re-read up-to-date N number of data automatically；

Described up-to-date N number of data being normalized by normalization, it is interval that the data after normalization are distributed in [0.1,0.9]；

According to gray model, the data after described normalization are passed through the Accumulating generation new data sample data as radial base neural net；

It is input to, as sample input data, the nervus opticus network trained by the new data after gray model Accumulating generation using described, matching through nervus opticus network obtains fitting data, this fitting data is carried out renormalization process and final prediction data can be obtained, this prediction data is stored and exports.

3. a kind of PM2.5 Concentration Testing based on amphineura network and Forecasting Methodology as claimed in claim 2, it is characterised in that: described step 2) in, the training step of described first nerves network includes:

Step 2.1, the data collection interval setting PM2.5 sensor and times of collection, data collection interval and times of collection collection according to setting organize measurement data more, gather the official standard data that many groups synchronize, using training data as BP neutral net of described measurement data and normal data simultaneously；

Step 2.2, set BP neutral net as three layers: input layer, hidden layer and output layer, set the node number of input layer and hidden layer, and it is identical with input layer to set output layer node number.

Step 2.3, setting the transmission function of hidden layer as Log-Sigmiod function, the transmission function of output layer is linear function, and wherein Log-Sigmiod function computing formula is as follows:

$\log sig\left(n\right)=\frac{1}{1+e^{-n}}$

Step 2.4, with little random number, weights and biasing are initialized, to ensure that Network Dept. is saturated by big weights input, concurrently set the anticipation error minima of network, maximum iteration time and learning rate；

The normal data of described official, as input, is input to BP neutral net as target by step 2.5, the measurement data recorded by described PM2.5 sensor, calculates error, according to error transfer factor weights；

Step 2.6, judge whether convergence, when error is less than anticipation error minima, algorithmic statement；Or terminate algorithm when reaching maximum iteration time；

Step 2.7, input training data carry out simulating, verifying, it is determined that network training completes.

4. a kind of PM2.5 Concentration Testing based on amphineura network and Forecasting Methodology as claimed in claim 2 or claim 3, it is characterised in that: described step 3) in, the training step of described nervus opticus network includes:

Step 3.1, by being obtained the measurement data of corresponding localization by the BP neutral net that trains by the measurement data of PM2.5 sensor acquisition, the normal data of the measurement data of localization and collection is all normalized and obtains measurement data and normal data after normalization.Normalization formula is as follows:

$y=0.1+\frac{0.8(x-x_{\min })}{(x_{max}-x)}$

In formula: x is the measurement data of described localization, x_minAnd x_maxRespectively often organizing the minima in data and maximum, y is the measurement data after normalization, is distributed in [0.1,0.9] interval；

Step 3.2, according to gray model, by the measurement data after described normalization by one group of new data of Accumulating generation, Accumulating generation formula is as follows:

Measurement data after note normalization is:

X⁽⁰⁾={ x⁽⁰⁾(1),x⁽⁰⁾(2),...x⁽⁰⁾(n)}

New data after note Accumulating generation is:

X⁽¹⁾={ x⁽¹⁾(1),x⁽¹⁾(2),...x⁽¹⁾(n)}

Wherein

$X^{\left(1\right)}\left(k\right)=\underset{i=1}{\overset{k}{\Σ}}{x}^{\left(0\right)}\left(i\right),k=1,2,...n.$

Using this new data training data as radial base neural net；

Step 3.3, set radial base neural net as three layers: input layer, hidden layer and output layer, set the node number of input layer and hidden layer, and set output layer as a node.

Step 3.4, setting the excitation function of hidden layer as Gaussian function, set the transmission function of output layer as linear function, wherein Gaussian function formula is as follows:

$\mathrm{\φ}\left(\right||X_k-X_i|\left|\right)=\exp (-\frac{n}{{d_{\max }}^2}||X_k-X_i|{|}^2),i=1,2,...,n$

In formula: X_kFor training sample, X_iFor individual cluster centre, d_maxFor the ultimate range between selected center, n is the node number of hidden layer；

Output result is as follows:

$y=\underset{i=1}{\overset{N}{\Σ}}{\mathrm{\ω}}_i\mathrm{\φ}(X_k,X_i)-x^{\left(1\right)}\left(n\right)$

Step 3.5, being inputted as the sample of radial base neural net by the described new data by obtaining after gray model Accumulating generation, normalization normal data exports as target, and radial base neural net is trained；

Step 3.6, choose cluster centre by K-means clustering algorithm.Several different samples are randomly choosed as initial cluster centre inputting from described sample, one sample of stochastic inputs, calculates this input sample nearest apart from which cluster centre, just it is classified as the same class of this cluster centre, repetitive operation, updates cluster centre；

Whether step 3.7, evaluation algorithm restrain, when cluster centre no longer changes or the threshold value less less than, and algorithmic statement.If it is determined that not convergence, otherwise forward step 5 to and continue iteration, the cluster centre finally determined during end；

Step 3.8, determine cluster centre after, with the new data obtained by gray model as input, normalized normal data as output training network, study obtain standard deviation and weights, wherein standard deviation formula is as follows:

$\mathrm{\σ}=\frac{d_{max}}{\sqrt{2n}}$

Step 3.9, input training data carry out simulating, verifying, it is determined that network training completes.